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An example is given here:

http://en.wikipedia.org/wiki/Non-Borel_set

Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated.

Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set.

See http://en.wikipedia.org/wiki/Non-measurable_set

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โˆ™ 2009-03-30 07:02:19
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Q: Give an example of a subset of R that is not a Borel set?
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